A brief description of the options to reach L'Aquila from Rome and Pescara can be found at the webpage of the University of L'Aquila under "Practical Information". The nearest airports are Rome Fiumicino (FCO), Rome Ciampino (CIA) and the Abbruzzo International Airport Pescara (PSR).
At all airports one has the option to rent a car. To reach L'Aquila from Rome and Pescara via the connecting Tollways is relatively easy. The transfer to L'Aquila via public transport takes about 2.5 - 3 hours. Please note, that you need to buy the corresponding ticket before you enter the train or bus. Most connections and timetables can be found in the web:

Rome Fiumicino Airport to L'Aquila

• Metropolitan train FR1 from Fiumicino Aeroporto to Tiburtina Station (timetable); takes about 45min, goes every 15min, ticket price 5.50€
• ARPA Bus from Roma Tiburtina Station (Staz. Tiburtina) to L'Aquila - Terminal Bus Collemagio (timetable); takes about 1h40min, goes every hour, ticket price ca. 10€

Rome Ciampino Airport to L'Aquila

• Schiaffini bus to Roma Anagnina Subway Station (timetable); takes about 15min, ticket price 1€
    and
• Metro A from Roma Anagnina Subway Station to Roma Termini Station; takes about 1h
    or
• Terravision shuttle from Ciampino airport to Roma Termini Station; only for passengers of selected airlines (more information), takes about 1h, ticket price 8€
• Metro B from Roma Termini Station to Roma Tiburtina Station; takes about 10min
• ARPA Bus from Roma Tiburtina Station (Staz. Tiburtina) to L'Aquila - Terminal Bus Collemagio (timetable)

A map of the subway and city railways of Rome can be downloaded as pdf-file (750kB).

Abbruzzo International Airport Pescara to L'Aquila

• Bus line 38 (bus lines) from Pasquale Liberi Airport to Central Railway Station (Stazione Centrale); takes about 10min, goes every 10min
• Bus from Pescara - Piazza della Repubblica (next to Central Railway Station) to L'Aquila - Terminal Bus Collemagio (timetable)
; takes about 1h50min

A bird's eye view by Google maps of the way from Terminal Bus Collemagio to the Castle of L'Aquila can be found here. Please note, that the ARPA station (for inter-city buses, e.g. to and from Rome) of Terminal Bus Collemagio is an underground station. There is an underground walkway (with underground escalators and "tapis roulant") to Piazza Duomo (downtown).
Please visit the website of AMA for a map of the Public bus transport lines (click and pull to access the zoom bottons of the map). There you can also find the timetables for all lines.